I think in part to match the literature on topological spaces, which I think usually does this. There may be various properties of dense embeddings into compact Hausdorff spaces that should be given here, besides any properties of arbitrary continuous maps to compact Hausdorff spaces.

]]>I made a few corrections at compactification.

Why are we using the less general notion, where the map to the compactification is required to be a dense embedding?

]]>added to *compactification* the statement of the uniqueness of compactifications for “almost compact topological spaces”